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ATOMIC ORIGINS OF MAGNETISM
ELECTRICITY AND MAGNETISM ARE TIED TOGETHER. ELECTRIC FIELD OR ELECTRICITY OCCURS SPONTANEOUSLY FROM ELECTRONIC CHARGES. MAGNETIC FIELD OR MAGNETISM IS A RESULT OF MOVING CHARGES. FROM AN ATOMIC VIEW OF MATTER, WE HAVE: ORBITAL MOTION OF THE ELECTRON, SPIN MOTION OF THE ELECTRON. THESE TWO ELECTRON MOTIONS ARE THE SOURCE OF MACROSCOPIC MAGNETIC PHENOMENA IN MATERIALS.
MAGNETIC VARIABLES
MAGNETIC FIELD STRENGTH (INTENSITY) IS REPRESENTED BY H (FIELD THAT RESULTS SOLELY FROM FREE CURRENT).
MAGNETIC MOMENT PER VOLUME IS MEASURED BY M (MAGNETIZATION). M RESULTS FROM THE TWO ATOMIC MOTIONS : ORBITAL AND SPIN MOTION OF THE ELECTRON.
B = H + 4pM (CGS)
MAGNETIC SUSCEPTIBILITY AND PERMEABILITY
THE MOST COMMON MAGNETIC EXPERIMENT IS TO APPLY A MAGNETIC FIELD TO A MATERIAL AND MEASURE THE MAGNETIZATION INDUCED BY THE FIELD. k = M/H m = B/H
SUSCEPTIBILTY
PERMEABILITY
m=1+4pk
MAGNETIC MATERIALS
FERROMAGNETISM : INTERACTION IS STRONGLY ATTRACTIVE TOWARD A MAGNETIC POLE,
PARAMAGNETISM : INTERACTION IS WEAKLY ATTRACTIVE,
DIAMAGNETISM : INTERACTION IS WEAKLY REPULSIVE.
MAGNETIC DOMAINS
AN ORDINARY PIECE OF IRON BELOW ITS CURIE TEMPERATURE YIELDS A MACROSCOPIC TOTAL MOMENT.
HOW IS IT THAT THIS PIECE OF IRON HAS NO MAGENTIC MOMENT? A MACROSCOPIC MAGNETIC MATERIAL WILL BREAK UP INTO DOMAINS.
AN OPTIMAL WALL THICKNESS l ~ (kTc / Ka)1/2 WITH A SURFACE ENERGY OF g ~ (kTcK / a)1/2 a - THE LATTICE SPACING, l - A FEW TENS OF NANOMETER, g - 1 erg / cm2.
HYSTERESIS
WHEN A FERROMAGNETIC MATERIAL IS MAGNETIZED BY AN INCREASING APPLIED FIELD AND THEN THE FIELD IS DECREASED, THE MAGNETIZATION DOES NOT FOLLOW THE INITIAL MAGNETIZATION CURVE OBTAINED DURING THE INCREASE. THIS IRREVERSIBILITY IS CALLED HYSTERESIS (DUE TO INTERNAL FRICTION).
PERMANENT MAGNETS (SUCH AS “REFRIGERATOR MAGNETS”) REQUIRE LARGE Ms, Mr, AND Hc.
HARD MAGNETS - Hc > 100 Oe SOFT MAGENTS - Hc < 10 Oe (MOTORS, GENERATORS), (TRANSFORMER CORES, ELECTRONIC CIRCUITS)
THE INITIAL MAGNETIZATION CURVE MAY BE DIVIDED INTO TWO REGIMES: RAYLEIGH LAW REGIME, MAGNETIZATION ROTATION.
THE LOW-FIELD BEHAVIOR OF THE INITIAL MAGNETIZATION IS GIVEN BY THE RAYLEIGH LAW, µ = µo + nH (B = µH)
WHERE µo AND n ARE THE RAYLEIGH CONSTANTS OF THE MATERIAL: 30 < µo < 105
0.5 < n < 1.2 x 107
AND B = µoH + nH2
HENCE THE PARABOLIC NATURE OF M VS. H AT LOW H.
THE BARKHAUSEN EFFECT IS DUE TO THE DOMAIN WALLS STICKING AT INCLUSIONS AS THEY ATTEMPT TO MOVE WITH CHANGING H. AT LARGE FIELDS,
M(H) = Ms (1 - a / H)
SMALL PARTICLE MAGNETISM
(1 µm OR LESS)
MAGNETISM OF SMALL FERROMAGNETIC PARTICLES IS DOMINATED BY TWO KEY FEATURES: - THERE IS SIZE UPPER LIMIT FOR SINGLE DOMAIN, - THERMAL ENERGY CAN DECOUPLE THE MAGNETIZATION FROM THE PARTICLE ITSELF TO GIVE RISE TO THE PHENOMENON OF SUPERPARAMAGNETISM. TWO CRITICAL SIZES ARISE FROM IT: - SINGLE DOMAIN SIZE,
- SUPERPARAMAGNETIC SIZE.
SINGLE-DOMAIN PARTICLES OF SIZE D (DIAMETER) THE ENERGY COST OF DOMAIN FORMATION EXCEEDS THE BENEFITS FROM DECREASING THE MAGNETOSTATIC ENERGY. THE MAGNETOSTATIC ENERGY ~ Ms2D3 THE TOTAL DOMAIN WALL ENERGY ~ gD2 SINGLE DOMAIN SIZE: Ds ~ g / Ms2
COERCIVITY OF SINGLE-DOMAIN PARTICLES
MAGNETIZATION REVERSAL IN SINGLE-DOMAIN PARTICLES OCCUR VIA ROTATION. IT PRODUCES A LARGE COERCIVITY IN COMPARISON TO MULTIDOMAIN SYSTEM. MAGNETIZATION CAN ROTATE BY COHERENT MOTION OF THE ATOMIC SPINS, BUT OTHER MOTIONS – FANNING AND CURLING – CAN OCCUR.
THE RESPONSE OF Ms TO AN APPLIED FIELD IS HINDERED BY THE ANISOTROPY (CRYSTALLINE, SHAPE, STRESS)
Ea = K sin2q THE APPLIED FIELD SUPPLIES A POTENTIAL ENERGY OF Ef = - Ms · H THE EQUILIBRIUM DIRECTION OF Ms RESULTS FROM THE MINIMUM OF THE TOTAL ENERGY: ETOTAL = Ea + Ef.
CONSIDER THE SITUATION IN WHICH THE APPLIED FIELD IS PERPENDICULAR TO THE EASY AXIS. THEN H q EASY AXIS ETOTAL = - MsH sinq + k sin2q sinq = MsH / 2K ETOTALMIN = - (MsH)2 / 2K + (MsH)2 / 4K
Ms
= - (MsH)2 / 4K
AND Hc = (2K) / Ms COERCIVITY
THE TWO CASES WE HAVE CONSIDERED REPRESENT EXTREMES OF THE POSSIBLE HYSTERESIS CURVES, TOTALLY CLOSED (NO HYSTERESIS) AND TOTALLY OPEN (SQUARE). VERY OFTEN WHEN DEALING WITH NANOPARTICLES, THE EASY AXIS ARE RANDOMLY ORIENTED. THE HYSTERESIS CURVE IS AN AVERAGE OVER ALL ORIENTATION. SOURCE OF THE ANISOTROPY K: CRYSTALLINE ANISOTROPY, SHAPE, STRESS, SURFACE ANISOTROPY.
SHAPE ANISOTROPY FOR NANOPARTICLES IS VERY LARGE EVEN FOR MODEST SHAPE RATIOS, c / a.
IT IS EASIER TO INDUCE A MAGNETIZATION ALONG A LONG DIRECTION OF A NONSPHERICAL NANOPARTICLE THAN ALONG A SHORT SINCE THE DEMAGNETIZING FIELD IS LESS IN THE LONG DIRECTION. FOR A PROLATE SPHEROID WITH MAJOR AXIS c GREATER THAN THE OTHER TWO AND EQUAL AXES OF LENGTH a, THE SHAPE ANISOTROPY IS Ks = (1/2) (Na – Nc) Ms2 WHERE Nc + 2Na = 4p SPHERE - Na = Nc, Ks = 0
PROLATE SPHEROID (c >> a) - Nc ~ 0, Na = 2p, Ks = 2p Ms2 THUS A LONG ROD OF IRON WITH Ms = 1714 emu / cm2 WOULD HAVE A SHAPE ANISOTROPY CONSTANT OF Ks = 1.85 x 107 erg / cm3 THIS IS SIGNIFICANTLY GREATER THAN CRYSTAL ANISOTROPY.
THE TOTAL MAGNETIZATION OF A FERROMAGNET Ms WILL PREFER TO LIE ALONG A SPECIAL DIRECTION CALLED THE EASY AXIS. THE ENERGY ASSOCIATED WITH THIS ALIGNMENT IS CALLED THE ANISOTROPY ENERGY Ea = K sin2q THERE ARE SEVERAL REASONS THAT ANISOTROPY MAY OCCUR: STRESS OR SHAPE (INDUCED) AND MAGENTOCRYSTALLINE ANISOTROPY (INTRINSIC).
MAGNETOCRYSTALLINE ANISOTROPY
THE EASE OF OBTAINING SATURATION MAGNETIZATION IS DIFFERENT FOR DIFFERENT CRYSTALLOGRAPHIC DIRECTIONS.
AN EXAMPLE IS A SINGLE CRYSTAL OF IRON FOR WHICH Ms IS MOST EASILY OBTAINED IN THE [100] DIRECTION, THEN LESS EASY FOR THE [110] DIRECTION, AND MOST DIFFICULT FOR THE [111] DIRECTIONS. THE [100] DIRECTION IS CALLED THE EASY DIRECTION WHICH IS IN THE DIRECTION OF SPONTANEOUS MAGNETIZATION WHEN BELOW Tc. FOR A UNIAXIAL MATERIAL WITH ONLY K1, IT CAN BE SHOWN THAT THE FIELD NECESSARY TO ROTATE THE MAGNETIZATION 90° AWAY FROM THE EASY AXIS IS H = 2K1 / Ms
THE PHYSICAL ORIGIN OF THE
MAGNETOCRYSTALLINE ANISOTROPY IS
THE COUPLING OF THE ELECTRON
SPINS, TO THE ELECTRON ORBIT, WHICH
IN TURN ARE COUPLED TO THE LATTICE.
FANNING
MAGNETIZATION REVERSAL BY THE FANNING MECHANISM IS RELEVANT IN CHAINS OF NANOPARTICLES OR HIGHLY ELONGATED NANOPARTICLES.
IN A CHAIN THE Ms VECTOR OF EACH NANOPARTICLE INTERACTS WITH ITS NEIGHBORS VIA THE MAGNETIC DIPOLAR INTERACTION. THUS THE DIPOLES LINE UP, NORTH TO SOUTH, AND LIKE TO REMAIN IN ALIGNMENT, HENCE CAUSING AN ANISOTROPY EVEN IF NO OTHERS EXIST. THIS IS CALLED AN INTERACTION ANISOTROPY. THE INCOHERENT REALIGNMENT IS CALLED FANNING. FANNING REVERSAL LEADS TO A SQUARE HYSTERESIS LOOP. THE Hc IS ONE-THIRD AS LARGE AS FOR A COHERENT REVERSAL Hc (FANNING) = p Ms / 6
CURLING IF THE ATOMIC SPINS ARE ALWAYS PERPENDICULAR TO A RADIUS VECTOR IN THE XY-PLANE, THIS IS CALLED CURLING.
INFINITELY LONG NANOPARTICLES
NO MAGNETOSTATIC ENERGY IS INVOLVED. THE REVERSAL VIA CURLING TAKES PLACE. FINITE NANOPARTICLES THE EXCHANGE INTERACTION IS MORE EFFECTIVE IN RESISTING THE REVERSAL, HENCE THE SMALL PARTICLES REVERSE COHERENTLY.
THE CROSSOVER BETWEEN CURLING AND COHERENT ROTATION OCCURS AT ROUGHLY 15 nm FOR IRON NANOPARTICLES.
SUPERPARAMAGNETISM
A LARGE TOTAL MOMENT IS BOUND RIGIDLY TO THE PARTICLE BELOW THE CURIE TEMPERATURE BY ONE OR MORE OF THE VARIETY OF ANISOTROPIES. THE ENERGY OF THIS BOND IS KV. WITH DECREASING PARTICLE SIZE, KV DECREASES UNTIL THE THERMAL ENERGY kT CAN DISRUPT BONDING OF THE TOTAL MOMENT TO THE PARTICLE.
THEN THIS MOMENT IS FREE TO MOVE AND RESPOND TO AN APPLIED FIELD INDEPENDENT OF THE PARTICLE.
µp = Ms V AN APPLIED FIELD WOULD TEND TO ALIGN THIS GIANT MOMENT (OR SUPERMOMENT) BUT kT WOULD FIGHT THE ALIGNMENT JUST AS IT DOES IN A PARAMAGNET.
SUPERPARAMAGNETISM HAS TWO KEY QUALITIES:
- LACK OF HYSTERESIS,
- UNIVERSAL CURVE OF M VS. H / T. THE ANISOTROPY ENERGY KV REPRESENTS AN ENERGY BARRIER TO THE TOTAL SPIN REORIENTATION; HENCE THE PROBABILITY FOR JUMPING THIS BARRIER IS ~ exp(-KV / kT) THE TIMESCALE FOR A SUCCESSFUL JUMP IS t = to exp(-KV / kT) WHERE to - ATTEMPT TIMESCALE = 10-9 s. IF Ms REVERSES AT TIMES SHORTER THAN THE EXPERIMENTAL TIMESCALES (10 s < t < 100 s), THE SYSTEM APPEARS SUPERPARAMAGNETIC.
THE CRITICAL VOLUME
Vsp = 25 kT / K
BY USING t ~ 100 s AND to = 10-9 s. E.G.
Co - Dsp = 7.6 nm
Fe - Dsp = 16 nm AT 300 K.
(Ds = 70 nm)
TB = KV / 25k, BLOCKING TEMPERATURE
T < TB FREE MOVEMENT OF µp = MsV IS BLOCKED BY THE ANISOTROPY
T > TB - SYSTEM APPEARS SUPERPARAMAGNETIC
THE COERCIVITY OF SMALL PARTICLES
AT LARGE SIZE, THE PARTICLES HAVE MANY DOMAINS, THUS MAGNETIZATION REVERSAL IS DOMINATED BY DOMAIN WALL MOTION, WHICH IS RELATIVELY EASY, HENCE THE COERCIVITY IS LOW. HOWEVER, AS PARTICLE SIZE DECREASES, THE COERCIVITY IS FOUND EMPIRICALLY TO FOLLOW
Hc = a + (b / D)
UNTIL SINGLE DOMAIN IS REACHED. THE LARGEST COERCIVITIES OCCUR AT THE SINGLE-DOMAIN SIZE. BELOW THIS, Hc FALLS OFF DUE TO THERMAL ACTIVATION OVER THE ANISOTROPY BARRIERS, LEADING TO Hc = (2K / Ms) [1 - (Dsp / D)3/2]
AND SUPERPARAMAGNETISM AT THE SUPERPARAMAGNETIC SIZE FOR WHICH Hc = 0.
MAGNETORESISTANCE
THE CHANGE IN RESISTANCE R OF A MATERIAL UNDER AN APPLIED MAGNETIC FIELD H IS KNOWN AS MAGNETO-RESISTANCE.
(Dr / r) = [R(H) – R(0)] / R(0)
KELVIN EXAMINED THE RESISTANCE OF AN IRON SAMPLE. HE FOUND: 0.2 % INCREASE IN THE RESISTANCE FOR LONGITUDINAL FIELD, 0.4 % DECREASE IN THE RESISTANCE FOR TRANSVERSE FIELD.
GIANT AND COLOSSAL MAGNETORESISTANCE
GIANT MAGNETORESISTANCE WAS DISCOVERED IN MATERIALS FABRICATED BY DEPOSITING ON A SUBSTRATE ALTERNATE LAYERS OF NANOMETER THICKNESS OF A FERROMAGNETIC MATERIAL AND A NONFERROMAGNETIC METAL.
THE ELECTRON SCATTERING DEPENDS ON THE ORIENTATION OF THE ELECTRON SPIN WITH RESPECT TO THE DIRECTION OF MAGNETIZATION
THE MAGNETORESISTANCE EFFECT IN THESE LAYERED MATERIALS IS A SENSITIVE DETECTOR OF DC MAGNETIC FIELDS AND ALREADY USED AS READING HEAD FOR MAGNETIC DISKS (MAGNETIC STORAGE DEVICES OR SENSING ELEMENTS IN MAGNETOMETERS). MATERIALS MADE OF SINGLE-DOMAIN FERROMAGNETIC NANOPARTICLES WITH RANDOMLY ORIENTED MAGNETIZATIONS EMBEDDED IN A NONMAGNETIC MATRIX DISPLAY GIANT MAGNETORESISTANCE.
MIXED VALENCE SYSTEM EXHIBITS VERY LARGE (COLOSSAL) MAGNETORESISTIVE EFFECTS. La0.67Ca0.33Mn Ox DISPLAYS MORE THAN A THOUSANDFOLD CHANGE IN RESISTANCE WITH 6-T DC MAGNETIC FIELD.
NANOCARBON FERROMAGNETS
IRON AND COBALT NANOPARTICLES ARE NECESSARY FOR THE NUCLEATION AND GROWTH OF CARBON NANOTUBES. NANOTUBE GROWTH INVOLVES TWO IRON NANOPARTICLES. A SMALL IRON PARTICLE SERVES AS A NUCLEUS AND A LARGER PARTICLE ENHANCES THE GROWTH.
THE CORECIVE FIELD INCREASES THREE TIMES WHEN TEMPERATURE IS REDUCED TO 4.2 K.
ELECTRICITY AND MAGNETISM ARE TIED TOGETHER. ELECTRIC FIELD OR ELECTRICITY OCCURS SPONTANEOUSLY FROM ELECTRONIC CHARGES. MAGNETIC FIELD OR MAGNETISM IS A RESULT OF MOVING CHARGES. FROM AN ATOMIC VIEW OF MATTER, WE HAVE: ORBITAL MOTION OF THE ELECTRON, SPIN MOTION OF THE ELECTRON. THESE TWO ELECTRON MOTIONS ARE THE SOURCE OF MACROSCOPIC MAGNETIC PHENOMENA IN MATERIALS.
MAGNETIC VARIABLES
MAGNETIC FIELD STRENGTH (INTENSITY) IS REPRESENTED BY H (FIELD THAT RESULTS SOLELY FROM FREE CURRENT).
MAGNETIC MOMENT PER VOLUME IS MEASURED BY M (MAGNETIZATION). M RESULTS FROM THE TWO ATOMIC MOTIONS : ORBITAL AND SPIN MOTION OF THE ELECTRON.
B = H + 4pM (CGS)
MAGNETIC SUSCEPTIBILITY AND PERMEABILITY
THE MOST COMMON MAGNETIC EXPERIMENT IS TO APPLY A MAGNETIC FIELD TO A MATERIAL AND MEASURE THE MAGNETIZATION INDUCED BY THE FIELD. k = M/H m = B/H
SUSCEPTIBILTY
PERMEABILITY
m=1+4pk
MAGNETIC MATERIALS
FERROMAGNETISM : INTERACTION IS STRONGLY ATTRACTIVE TOWARD A MAGNETIC POLE,
PARAMAGNETISM : INTERACTION IS WEAKLY ATTRACTIVE,
DIAMAGNETISM : INTERACTION IS WEAKLY REPULSIVE.
MAGNETIC DOMAINS
AN ORDINARY PIECE OF IRON BELOW ITS CURIE TEMPERATURE YIELDS A MACROSCOPIC TOTAL MOMENT.
HOW IS IT THAT THIS PIECE OF IRON HAS NO MAGENTIC MOMENT? A MACROSCOPIC MAGNETIC MATERIAL WILL BREAK UP INTO DOMAINS.
AN OPTIMAL WALL THICKNESS l ~ (kTc / Ka)1/2 WITH A SURFACE ENERGY OF g ~ (kTcK / a)1/2 a - THE LATTICE SPACING, l - A FEW TENS OF NANOMETER, g - 1 erg / cm2.
HYSTERESIS
WHEN A FERROMAGNETIC MATERIAL IS MAGNETIZED BY AN INCREASING APPLIED FIELD AND THEN THE FIELD IS DECREASED, THE MAGNETIZATION DOES NOT FOLLOW THE INITIAL MAGNETIZATION CURVE OBTAINED DURING THE INCREASE. THIS IRREVERSIBILITY IS CALLED HYSTERESIS (DUE TO INTERNAL FRICTION).
PERMANENT MAGNETS (SUCH AS “REFRIGERATOR MAGNETS”) REQUIRE LARGE Ms, Mr, AND Hc.
HARD MAGNETS - Hc > 100 Oe SOFT MAGENTS - Hc < 10 Oe (MOTORS, GENERATORS), (TRANSFORMER CORES, ELECTRONIC CIRCUITS)
THE INITIAL MAGNETIZATION CURVE MAY BE DIVIDED INTO TWO REGIMES: RAYLEIGH LAW REGIME, MAGNETIZATION ROTATION.
THE LOW-FIELD BEHAVIOR OF THE INITIAL MAGNETIZATION IS GIVEN BY THE RAYLEIGH LAW, µ = µo + nH (B = µH)
WHERE µo AND n ARE THE RAYLEIGH CONSTANTS OF THE MATERIAL: 30 < µo < 105
0.5 < n < 1.2 x 107
AND B = µoH + nH2
HENCE THE PARABOLIC NATURE OF M VS. H AT LOW H.
THE BARKHAUSEN EFFECT IS DUE TO THE DOMAIN WALLS STICKING AT INCLUSIONS AS THEY ATTEMPT TO MOVE WITH CHANGING H. AT LARGE FIELDS,
M(H) = Ms (1 - a / H)
SMALL PARTICLE MAGNETISM
(1 µm OR LESS)
MAGNETISM OF SMALL FERROMAGNETIC PARTICLES IS DOMINATED BY TWO KEY FEATURES: - THERE IS SIZE UPPER LIMIT FOR SINGLE DOMAIN, - THERMAL ENERGY CAN DECOUPLE THE MAGNETIZATION FROM THE PARTICLE ITSELF TO GIVE RISE TO THE PHENOMENON OF SUPERPARAMAGNETISM. TWO CRITICAL SIZES ARISE FROM IT: - SINGLE DOMAIN SIZE,
- SUPERPARAMAGNETIC SIZE.
SINGLE-DOMAIN PARTICLES OF SIZE D (DIAMETER) THE ENERGY COST OF DOMAIN FORMATION EXCEEDS THE BENEFITS FROM DECREASING THE MAGNETOSTATIC ENERGY. THE MAGNETOSTATIC ENERGY ~ Ms2D3 THE TOTAL DOMAIN WALL ENERGY ~ gD2 SINGLE DOMAIN SIZE: Ds ~ g / Ms2
COERCIVITY OF SINGLE-DOMAIN PARTICLES
MAGNETIZATION REVERSAL IN SINGLE-DOMAIN PARTICLES OCCUR VIA ROTATION. IT PRODUCES A LARGE COERCIVITY IN COMPARISON TO MULTIDOMAIN SYSTEM. MAGNETIZATION CAN ROTATE BY COHERENT MOTION OF THE ATOMIC SPINS, BUT OTHER MOTIONS – FANNING AND CURLING – CAN OCCUR.
THE RESPONSE OF Ms TO AN APPLIED FIELD IS HINDERED BY THE ANISOTROPY (CRYSTALLINE, SHAPE, STRESS)
Ea = K sin2q THE APPLIED FIELD SUPPLIES A POTENTIAL ENERGY OF Ef = - Ms · H THE EQUILIBRIUM DIRECTION OF Ms RESULTS FROM THE MINIMUM OF THE TOTAL ENERGY: ETOTAL = Ea + Ef.
CONSIDER THE SITUATION IN WHICH THE APPLIED FIELD IS PERPENDICULAR TO THE EASY AXIS. THEN H q EASY AXIS ETOTAL = - MsH sinq + k sin2q sinq = MsH / 2K ETOTALMIN = - (MsH)2 / 2K + (MsH)2 / 4K
Ms
= - (MsH)2 / 4K
AND Hc = (2K) / Ms COERCIVITY
THE TWO CASES WE HAVE CONSIDERED REPRESENT EXTREMES OF THE POSSIBLE HYSTERESIS CURVES, TOTALLY CLOSED (NO HYSTERESIS) AND TOTALLY OPEN (SQUARE). VERY OFTEN WHEN DEALING WITH NANOPARTICLES, THE EASY AXIS ARE RANDOMLY ORIENTED. THE HYSTERESIS CURVE IS AN AVERAGE OVER ALL ORIENTATION. SOURCE OF THE ANISOTROPY K: CRYSTALLINE ANISOTROPY, SHAPE, STRESS, SURFACE ANISOTROPY.
SHAPE ANISOTROPY FOR NANOPARTICLES IS VERY LARGE EVEN FOR MODEST SHAPE RATIOS, c / a.
IT IS EASIER TO INDUCE A MAGNETIZATION ALONG A LONG DIRECTION OF A NONSPHERICAL NANOPARTICLE THAN ALONG A SHORT SINCE THE DEMAGNETIZING FIELD IS LESS IN THE LONG DIRECTION. FOR A PROLATE SPHEROID WITH MAJOR AXIS c GREATER THAN THE OTHER TWO AND EQUAL AXES OF LENGTH a, THE SHAPE ANISOTROPY IS Ks = (1/2) (Na – Nc) Ms2 WHERE Nc + 2Na = 4p SPHERE - Na = Nc, Ks = 0
PROLATE SPHEROID (c >> a) - Nc ~ 0, Na = 2p, Ks = 2p Ms2 THUS A LONG ROD OF IRON WITH Ms = 1714 emu / cm2 WOULD HAVE A SHAPE ANISOTROPY CONSTANT OF Ks = 1.85 x 107 erg / cm3 THIS IS SIGNIFICANTLY GREATER THAN CRYSTAL ANISOTROPY.
THE TOTAL MAGNETIZATION OF A FERROMAGNET Ms WILL PREFER TO LIE ALONG A SPECIAL DIRECTION CALLED THE EASY AXIS. THE ENERGY ASSOCIATED WITH THIS ALIGNMENT IS CALLED THE ANISOTROPY ENERGY Ea = K sin2q THERE ARE SEVERAL REASONS THAT ANISOTROPY MAY OCCUR: STRESS OR SHAPE (INDUCED) AND MAGENTOCRYSTALLINE ANISOTROPY (INTRINSIC).
MAGNETOCRYSTALLINE ANISOTROPY
THE EASE OF OBTAINING SATURATION MAGNETIZATION IS DIFFERENT FOR DIFFERENT CRYSTALLOGRAPHIC DIRECTIONS.
AN EXAMPLE IS A SINGLE CRYSTAL OF IRON FOR WHICH Ms IS MOST EASILY OBTAINED IN THE [100] DIRECTION, THEN LESS EASY FOR THE [110] DIRECTION, AND MOST DIFFICULT FOR THE [111] DIRECTIONS. THE [100] DIRECTION IS CALLED THE EASY DIRECTION WHICH IS IN THE DIRECTION OF SPONTANEOUS MAGNETIZATION WHEN BELOW Tc. FOR A UNIAXIAL MATERIAL WITH ONLY K1, IT CAN BE SHOWN THAT THE FIELD NECESSARY TO ROTATE THE MAGNETIZATION 90° AWAY FROM THE EASY AXIS IS H = 2K1 / Ms
THE PHYSICAL ORIGIN OF THE
MAGNETOCRYSTALLINE ANISOTROPY IS
THE COUPLING OF THE ELECTRON
SPINS, TO THE ELECTRON ORBIT, WHICH
IN TURN ARE COUPLED TO THE LATTICE.
FANNING
MAGNETIZATION REVERSAL BY THE FANNING MECHANISM IS RELEVANT IN CHAINS OF NANOPARTICLES OR HIGHLY ELONGATED NANOPARTICLES.
IN A CHAIN THE Ms VECTOR OF EACH NANOPARTICLE INTERACTS WITH ITS NEIGHBORS VIA THE MAGNETIC DIPOLAR INTERACTION. THUS THE DIPOLES LINE UP, NORTH TO SOUTH, AND LIKE TO REMAIN IN ALIGNMENT, HENCE CAUSING AN ANISOTROPY EVEN IF NO OTHERS EXIST. THIS IS CALLED AN INTERACTION ANISOTROPY. THE INCOHERENT REALIGNMENT IS CALLED FANNING. FANNING REVERSAL LEADS TO A SQUARE HYSTERESIS LOOP. THE Hc IS ONE-THIRD AS LARGE AS FOR A COHERENT REVERSAL Hc (FANNING) = p Ms / 6
CURLING IF THE ATOMIC SPINS ARE ALWAYS PERPENDICULAR TO A RADIUS VECTOR IN THE XY-PLANE, THIS IS CALLED CURLING.
INFINITELY LONG NANOPARTICLES
NO MAGNETOSTATIC ENERGY IS INVOLVED. THE REVERSAL VIA CURLING TAKES PLACE. FINITE NANOPARTICLES THE EXCHANGE INTERACTION IS MORE EFFECTIVE IN RESISTING THE REVERSAL, HENCE THE SMALL PARTICLES REVERSE COHERENTLY.
THE CROSSOVER BETWEEN CURLING AND COHERENT ROTATION OCCURS AT ROUGHLY 15 nm FOR IRON NANOPARTICLES.
SUPERPARAMAGNETISM
A LARGE TOTAL MOMENT IS BOUND RIGIDLY TO THE PARTICLE BELOW THE CURIE TEMPERATURE BY ONE OR MORE OF THE VARIETY OF ANISOTROPIES. THE ENERGY OF THIS BOND IS KV. WITH DECREASING PARTICLE SIZE, KV DECREASES UNTIL THE THERMAL ENERGY kT CAN DISRUPT BONDING OF THE TOTAL MOMENT TO THE PARTICLE.
THEN THIS MOMENT IS FREE TO MOVE AND RESPOND TO AN APPLIED FIELD INDEPENDENT OF THE PARTICLE.
µp = Ms V AN APPLIED FIELD WOULD TEND TO ALIGN THIS GIANT MOMENT (OR SUPERMOMENT) BUT kT WOULD FIGHT THE ALIGNMENT JUST AS IT DOES IN A PARAMAGNET.
SUPERPARAMAGNETISM HAS TWO KEY QUALITIES:
- LACK OF HYSTERESIS,
- UNIVERSAL CURVE OF M VS. H / T. THE ANISOTROPY ENERGY KV REPRESENTS AN ENERGY BARRIER TO THE TOTAL SPIN REORIENTATION; HENCE THE PROBABILITY FOR JUMPING THIS BARRIER IS ~ exp(-KV / kT) THE TIMESCALE FOR A SUCCESSFUL JUMP IS t = to exp(-KV / kT) WHERE to - ATTEMPT TIMESCALE = 10-9 s. IF Ms REVERSES AT TIMES SHORTER THAN THE EXPERIMENTAL TIMESCALES (10 s < t < 100 s), THE SYSTEM APPEARS SUPERPARAMAGNETIC.
THE CRITICAL VOLUME
Vsp = 25 kT / K
BY USING t ~ 100 s AND to = 10-9 s. E.G.
Co - Dsp = 7.6 nm
Fe - Dsp = 16 nm AT 300 K.
(Ds = 70 nm)
TB = KV / 25k, BLOCKING TEMPERATURE
T < TB FREE MOVEMENT OF µp = MsV IS BLOCKED BY THE ANISOTROPY
T > TB - SYSTEM APPEARS SUPERPARAMAGNETIC
THE COERCIVITY OF SMALL PARTICLES
AT LARGE SIZE, THE PARTICLES HAVE MANY DOMAINS, THUS MAGNETIZATION REVERSAL IS DOMINATED BY DOMAIN WALL MOTION, WHICH IS RELATIVELY EASY, HENCE THE COERCIVITY IS LOW. HOWEVER, AS PARTICLE SIZE DECREASES, THE COERCIVITY IS FOUND EMPIRICALLY TO FOLLOW
Hc = a + (b / D)
UNTIL SINGLE DOMAIN IS REACHED. THE LARGEST COERCIVITIES OCCUR AT THE SINGLE-DOMAIN SIZE. BELOW THIS, Hc FALLS OFF DUE TO THERMAL ACTIVATION OVER THE ANISOTROPY BARRIERS, LEADING TO Hc = (2K / Ms) [1 - (Dsp / D)3/2]
AND SUPERPARAMAGNETISM AT THE SUPERPARAMAGNETIC SIZE FOR WHICH Hc = 0.
MAGNETORESISTANCE
THE CHANGE IN RESISTANCE R OF A MATERIAL UNDER AN APPLIED MAGNETIC FIELD H IS KNOWN AS MAGNETO-RESISTANCE.
(Dr / r) = [R(H) – R(0)] / R(0)
KELVIN EXAMINED THE RESISTANCE OF AN IRON SAMPLE. HE FOUND: 0.2 % INCREASE IN THE RESISTANCE FOR LONGITUDINAL FIELD, 0.4 % DECREASE IN THE RESISTANCE FOR TRANSVERSE FIELD.
GIANT AND COLOSSAL MAGNETORESISTANCE
GIANT MAGNETORESISTANCE WAS DISCOVERED IN MATERIALS FABRICATED BY DEPOSITING ON A SUBSTRATE ALTERNATE LAYERS OF NANOMETER THICKNESS OF A FERROMAGNETIC MATERIAL AND A NONFERROMAGNETIC METAL.
THE ELECTRON SCATTERING DEPENDS ON THE ORIENTATION OF THE ELECTRON SPIN WITH RESPECT TO THE DIRECTION OF MAGNETIZATION
THE MAGNETORESISTANCE EFFECT IN THESE LAYERED MATERIALS IS A SENSITIVE DETECTOR OF DC MAGNETIC FIELDS AND ALREADY USED AS READING HEAD FOR MAGNETIC DISKS (MAGNETIC STORAGE DEVICES OR SENSING ELEMENTS IN MAGNETOMETERS). MATERIALS MADE OF SINGLE-DOMAIN FERROMAGNETIC NANOPARTICLES WITH RANDOMLY ORIENTED MAGNETIZATIONS EMBEDDED IN A NONMAGNETIC MATRIX DISPLAY GIANT MAGNETORESISTANCE.
MIXED VALENCE SYSTEM EXHIBITS VERY LARGE (COLOSSAL) MAGNETORESISTIVE EFFECTS. La0.67Ca0.33Mn Ox DISPLAYS MORE THAN A THOUSANDFOLD CHANGE IN RESISTANCE WITH 6-T DC MAGNETIC FIELD.
NANOCARBON FERROMAGNETS
IRON AND COBALT NANOPARTICLES ARE NECESSARY FOR THE NUCLEATION AND GROWTH OF CARBON NANOTUBES. NANOTUBE GROWTH INVOLVES TWO IRON NANOPARTICLES. A SMALL IRON PARTICLE SERVES AS A NUCLEUS AND A LARGER PARTICLE ENHANCES THE GROWTH.
THE CORECIVE FIELD INCREASES THREE TIMES WHEN TEMPERATURE IS REDUCED TO 4.2 K.
